Probabilistic Graphical Models 10-708, Spring 2017

https://www.cs.cmu.edu/~epxing/Class/10708-17/slides/lecture1-Introduction.pdf

 

Computational and CS orientated => DK and NF's book

Statistical and easier one => Jordan's book

MLAPP => also a good book

 

HWs => Theory, algorithm design and implementation. Very heavy.

 

N copies of data.

subscript means the dims of features.

 

 

 

 

 bottom right figures

 

 

a given presentation + inference => enough for some tasks

learn a representation => a more adv. task

 

M* = argmax (m \in M) F(D;m)

M*: best representation

m: one representation

F: score function

D: data

 

 

 

 

 one simple case: every random variable X_n is binary: X_n \in {0,1}

O(exp(n)) => bad algorithm

 

↓↓↓↓↓↓↓↓↓↓(invite a biologist)↓↓↓↓↓↓↓↓↓↓↓

categorize

add pathways

 

 

18 vs 2^8

 

 

A factorization rule. two resources of variables.

 

 

 

 

 

 

 

 

 

 

PGM => conditional distribution

GM => pm.Deterministic

 

 

 If I have P(A,B), how to proof A is independent of B?

Method 1: defactorize P(A,B) = P(A)*P(B)

Method 2: build a graph like the one above, and A and B are automatically independent

 

 

 

 

Yellow ⊥  Orange | Graph

the yellow node is only linked to its parents, children, and children's coparents (greeen nodes)

⊥: indenpendency

 

 

 

 

 

 

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DARPA grand challenge

 

NLP

 

biostats